DOCSLIB.ORG

'Small-World-Ness': a Quantitative Method for Determining Canonical Network Equivalence

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
'Small-World-Ness': a Quantitative Method for Determining Canonical Network Equivalence This is a repository copy of Network 'small-world-ness': a quantitative method for determining canonical network equivalence. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/10308/ Article: Humphries, M.D. and Gurney, K. (2008) Network 'small-world-ness': a quantitative method for determining canonical network equivalence. Plos One, 3 (4). Art No.e0002051. ISSN 1932-6203 https://doi.org/10.1371/journal.pone.0002051 Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request. [email protected] https://eprints.whiterose.ac.uk/ Network ‘Small-World-Ness’: A Quantitative Method for Determining Canonical Network Equivalence Mark D. Humphries*, Kevin Gurney Adaptive Behaviour Research Group, Department of Psychology, University of Sheffield, Sheffield, United Kingdom Abstract Background: Many technological, biological, social, and information networks fall into the broad class of ‘small-world’ networks: they have tightly interconnected clusters of nodes, and a shortest mean path length that is similar to a matched random graph (same number of nodes and edges). This semi-quantitative definition leads to a categorical distinction (‘small/not-small’) rather than a quantitative, continuous grading of networks, and can lead to uncertainty about a network’s small-world status. Moreover, systems described by small-world networks are often studied using an equivalent canonical network model – the Watts-Strogatz (WS) model. However, the process of establishing an equivalent WS model is imprecise and there is a pressing need to discover ways in which this equivalence may be quantified. Methodology/Principal Findings: We defined a precise measure of ‘small-world-ness’ S based on the trade off between high local clustering and short path length. A network is now deemed a ‘small-world’ if S.1 - an assertion which may be tested statistically. We then examined the behavior of S on a large data-set of real-world systems. We found that all these systems were linked by a linear relationship between their S values and the network size n. Moreover, we show a method for assigning a unique Watts-Strogatz (WS) model to any real-world network, and show analytically that the WS models associated with our sample of networks also show linearity between S and n. Linearity between S and n is not, however, inevitable, and neither is S maximal for an arbitrary network of given size. Linearity may, however, be explained by a common limiting growth process. Conclusions/Significance: We have shown how the notion of a small-world network may be quantified. Several key properties of the metric are described and the use of WS canonical models is placed on a more secure footing. Citation: Humphries MD, Gurney K (2008) Network ‘Small-World-Ness’: A Quantitative Method for Determining Canonical Network Equivalence. PLoS ONE 3(4): e0002051. doi:10.1371/journal.pone.0002051 Editor: Olaf Sporns, Indiana University, United States of America Received November 21, 2007; Accepted March 16, 2008; Published April 30, 2008 Copyright: ß 2008 Humphries, Gurney. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: MDH acknowledges support by the EU Framework 6 IST-027819-IP (ICEA) project. KG acknowledges the support of EPSRC grant EP/C516303/1. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: [email protected] Introduction However, the existing ‘small-world’ definition is a categorical one, and breaks the continuum of network topologies into the Networks are widely used to both represent real-world systems three classes of regular, random, and small-world networks, with for topological study [1] and as a substrate for modeling their the latter being the broadest. It is unclear to what extent the real- dynamics [2]. Many real technological, biological, social, and world systems in the small-world class have common network information networks fall into the broad class of ‘small-world’ properties and to what specific point in the ‘‘middle-ground’’ networks [3], a middle ground between regular and random (between random and regular) a network generating model must networks: they have high local clustering of elements, like regular be tuned to genuinely capture the topology of such systems. Here networks, but also short path lengths between elements, like we explore a continuous, quantitative, measure of ‘small-world- random networks. Membership of the ‘small-world’ network class ness’, with the aim of overcoming these inadequacies in the also implies that the corresponding systems have dynamic current theory of small-world networks. properties different from those of equivalent random or regular networks [3–7]. Network formalism One popular method for studying small-world networks is to use When describing a real-world system as a network, each an equivalent network model to generate other similar instances of element of the system is represented by a vertex or node, and the class of systems under study. Such generating models may also relationships or interactions between elements are represented by possess analytic properties that, we assume, may be extrapolated to edges between nodes. Two nodes are said to be neighbors if they the target system. One canonical model used as a candidate for are connected by an edge, and the degree ki of node i is the number network equivalence is the original Watts-Strogatz (WS) model, of neighbors it has. The minimum path length between two nodes is which has been used as a substrate for studying dynamics in the the minimum number of edges that must be traversed to get from diverse fields of ecology [8], economics [9,10], epidemiology one node to the other. The mean value of the minimum path [11,12], and neuroscience [13]. length over all node pairs will be denoted by L. PLoS ONE | www.plosone.org 1 April 2008 | Volume 3 | Issue 4 | e0002051 Network ‘Small-World-Ness’ A key concept in defining small-worlds networks is that of The categorical definition of small-world network above implies $ D& D. ‘clustering’ which measures the extent to which the neighbors of a lg 1 and cg 1, which, in turn, gives S 1. We can, therefore, node are also interconnected. Watts and Strogatz [3] defined the now make a quantitative categorical definition of a ‘small-world’ ws clustering coefficient ci of node i by network Definition 2. A network is said to be a small-world network if 2E SD.1 ws~ i ci 1 ws ki ki{1 ð Þ A similar definition may also be given with respect to S . ðÞ However, notwithstanding the new categorical definition, we where Ei is the number of edges between the neighbors of i. The wish to emphasize here the utility of using a continuously graded ws ws clustering coefficient of the network C is then the mean of ci notion of small-world-ness. We go on, therefore, to analyze the over all nodes. An alternative definition of network clustering in properties of the new metrics, and apply them to real-world data common use [14], based on transitivity, is expressed by for the first time (in [16] we originally proposed this metric as a tool for comparing theoretical neuroanatomy models; its subse- 3|number of triangles quent adoption by others [17,18,19] motivated us to consider its CD~ , 2 theoretical and empirical applications as a universal metric). number of paths of length 2 ð Þ where a ‘triangle’ is a set of three nodes in which each contacts the Results other two. Both capture intuitive notions of clustering but, though often in good agreement, values for Cws and CD can differ by an New metrics behave as required with the Watts-Strogatz order of magnitude for some networks. We consider mainly CD model D here, but report where using Cws leads to different results. We first checked that the metric S behaves as required on the A network G with n nodes and m edges is a small-world network canonical Watts-Strogatz (WS) model of small-world generation [3] if it has a similar path length but greater clustering of nodes [3]. The WS model begins with a ring of n nodes, each node than an equivalent Erdo¨s-Re´nyi (E–R) random graph [15] with connected to its nearest neighbors out to some range K. Each edge the same m and n (an E–R graph is constructed by uniquely in turn is ‘re-wired’ to a new target node with probability p assigning each edge to a node pair with uniform probability). More (Figure 1A). Values of p = 0 and p = 1 give regular and random D networks, respectively, with intermediate p values resulting in formally, let Lg be the mean shortest path length of G and Cg its D ‘small-world’ networks that share properties of both provided that clustering coefficient using (2).
Load more

Recommended publications
  • Simplified Computational Model for Generating Bio- Logical Networks
    Simplified Computational Model for Generating Bio- logical Networks† Matthew H J Bailey,∗ David Ormrod Morley,∗ and Mark Wilson∗ A method to generate and simulate biological networks is discussed. An expanded Wooten- Winer-Weaire bond switching methods is proposed which allows for a distribution of node degrees in the network while conserving the mean average node degree. The networks are characterised in terms of their polygon structure and assortativities (a measure of local ordering). A wide range of experimental images are analysed and the underlying networks quantified in an analogous manner. Limitations in obtaining the network structure are discussed. A “network landscape” of the experimentally observed and simulated networks is constructed from the underlying metrics. The enhanced bond switching algorithm is able to generate networks spanning the full range of experimental observations. Two dimensional random networks are observed in a range of 17 contexts across considerably different length scales in nature: to be limited to avoid damaging the delicate networks . How- from nanometres, in the form of amorphous graphene; to me- ever, even when a high-quality image is obtained, there is further tres, in the form of the Giant’s causeway; to tens of kilometres, in difficulty in analysis. For example, each edge in a network is a the form of geopolitical borders 1–3. A framework for describing complex molecule made up of tens of thousands of atoms which these continuous random networks for chemical systems was first may not lie strictly in a single plane. In addition, the most inter- introduced by Zachariasen to describe silica-like glasses, and has esting dynamic behaviour often occurs over very long timescales proved to be extremely versatile in the years since 4, being used to – potentially decades.
    [Show full text]
  • Biological Network Approaches and Applications in Rare Disease Studies
    G C A T T A C G G C A T genes Review Biological Network Approaches and Applications in Rare Disease Studies Peng Zhang 1,* and Yuval Itan 2,3 1 St. Giles Laboratory of Human Genetics of Infectious Diseases, Rockefeller Branch, The Rockefeller University, New York, NY 10065, USA 2 The Charles Bronfman Institute for Personalized Medicine, Icahn School of Medicine at Mount Sinai, New York, NY 10029, USA; [email protected] 3 Department of Genetics and Genomic Sciences, Icahn School of Medicine at Mount Sinai, New York, NY 10029, USA * Correspondence: [email protected]; Tel.: +1-646-830-6622 Received: 3 September 2019; Accepted: 10 October 2019; Published: 12 October 2019 Abstract: Network biology has the capability to integrate, represent, interpret, and model complex biological systems by collectively accommodating biological omics data, biological interactions and associations, graph theory, statistical measures, and visualizations. Biological networks have recently been shown to be very useful for studies that decipher biological mechanisms and disease etiologies and for studies that predict therapeutic responses, at both the molecular and system levels. In this review, we briefly summarize the general framework of biological network studies, including data resources, network construction methods, statistical measures, network topological properties, and visualization tools. We also introduce several recent biological network applications and methods for the studies of rare diseases. Keywords: biological network; bioinformatics; database; software; application; rare diseases 1. Introduction Network biology provides insights into complex biological systems and can reveal informative patterns within these systems through the integration of biological omics data (e.g., genome, transcriptome, proteome, and metabolome) and biological interactome data (e.g., protein-protein interactions and gene-gene associations).
    [Show full text]
  • Denoising Large-Scale Biological Data Using Network Filters
    Kavran and Clauset BMC Bioinformatics (2021) 22:157 https://doi.org/10.1186/s12859‑021‑04075‑x RESEARCH ARTICLE Open Access Denoising large‑scale biological data using network flters Andrew J. Kavran1,2 and Aaron Clauset2,3,4* *Correspondence: [email protected] Abstract 2 BioFrontiers Institute, Background: Large-scale biological data sets are often contaminated by noise, which University of Colorado, Boulder, CO, USA can impede accurate inferences about underlying processes. Such measurement Full list of author information noise can arise from endogenous biological factors like cell cycle and life history vari- is available at the end of the ation, and from exogenous technical factors like sample preparation and instrument article variation. Results: We describe a general method for automatically reducing noise in large- scale biological data sets. This method uses an interaction network to identify groups of correlated or anti-correlated measurements that can be combined or “fltered” to better recover an underlying biological signal. Similar to the process of denoising an image, a single network flter may be applied to an entire system, or the system may be frst decomposed into distinct modules and a diferent flter applied to each. Applied to synthetic data with known network structure and signal, network flters accurately reduce noise across a wide range of noise levels and structures. Applied to a machine learning task of predicting changes in human protein expression in healthy and cancer- ous tissues, network fltering prior to training increases accuracy up to 43% compared to using unfltered data. Conclusions: Network flters are a general way to denoise biological data and can account for both correlation and anti-correlation between diferent measurements.
    [Show full text]
  • Introduction to Graph Theory
    Introduction to Graph Theory Proteomes Interactomes and Biological Networks Department of Pharmacy and Emidio Capriotti Biotechnology (FaBiT) http://biofold.org/ University of Bologna Historical Perspective With the Seven Bridges of Königsberg problem, Euler in 1737 laid the foundations of the graph theory. Simon Kneebone – simonkneebone.com • Find path (Eulerian Path) that traverses all the Pregel’s bridges. • Find walk (Eulerian Circuit) that traverses all the Pregel’s bridges and has the same starting and ending point. Solution Describe the problem as a graph where the nodes represent the 4 locations and the edges correspond to the bridges Northern Bank Island 1 Island 2 Southern Bank Eulerian path exists only if zero or 2 nodes are connected by an odd number of bridges. Eulerian circuit exists only if zero nodes are connected by an odd number of bridges. Graph Definition A graph is a pair G=(V,E) consisting of two sets: • V is a set of elements called Nodes or Vertices. • E is a set of pairs (vi,vj) where vi∊V and vj∊V. The pairs E are links between two nodes and are called Edges A V = {A; B; C; D} B C E = {(A,B); (A,C); (B,C); (B,D); (C,D)} D Undirected Graph Undirected graph is a network where the relationship between nodes are symmetric. D V = {Group of People} A B C E E = {Pairs of Friends} F Directed Graph Directed graph is a network where the relationship between nodes are asymmetric. In this case the edges are directed lines. B C V = {Group of Animals} A D E E = {Pray/Predator Relationships} F G Signed Directed Graph Signed Directed graph is a network where the relationship between nodes are asymmetric and have positive or negative associated signs RecKinase RecCAMP_act RecCAMP_de Galpha_bnd Galpha_act_bnd + − C E − V = {Group of Genes} A B + E = {Activation/Inhibition Relationships} D Graph and Networks Graphs can be used to represent any observed network.
    [Show full text]
  • Visual Analytics for Multimodal Social Network Analysis: a Design Study with Social Scientists
    Visual Analytics for Multimodal Social Network Analysis: A Design Study with Social Scientists Sohaib Ghani, Student member, IEEE, Bum chul Kwon, Student member, IEEE, Seungyoon Lee, Ji Soo Yi, Member, IEEE, and Niklas Elmqvist, Senior member, IEEE Fig. 1. Four design sketches for visualizing multimodal social networks, evolved through discussion between social network experts and visual analytics experts. Early designs (top two) focus on splitting node-link diagrams into separate spaces, whereas the latter (bottom left) use vertical bands while maintaining compatibility with node-link diagrams (bottom right). Abstract—Social network analysis (SNA) is becoming increasingly concerned not only with actors and their relations, but also with distinguishing between different types of such entities. For example, social scientists may want to investigate asymmetric relations in organizations with strict chains of command, or incorporate non-actors such as conferences and projects when analyzing co- authorship patterns. Multimodal social networks are those where actors and relations belong to different types, or modes, and multimodal social network analysis (mSNA) is accordingly SNA for such networks. In this paper, we present a design study that we conducted with several social scientist collaborators on how to support mSNA using visual analytics tools. Based on an open- ended, formative design process, we devised a visual representation called parallel node-link bands (PNLBs) that splits modes into separate bands and renders connections between adjacent ones, similar to the list view in Jigsaw. We then used the tool in a qualitative evaluation involving five social scientists whose feedback informed a second design phase that incorporated additional network metrics.
    [Show full text]
  • An Integrative Approach to Modeling Biological Networks 1 Introduction
    Journal of Integrative Bioinformatics, 7(3):120, 2010 http://journal.imbio.de An integrative approach to modeling biological networks Vesna Memisevˇ ic´ 1, Tijana Milenkovic´ 1, and Natasaˇ Prˇzulj2,∗ 1Department of Computer Science, University of California, Irvine, CA 92697-3435, USA 2Department of Computing, Imperial College London, London, SW7 2AZ, UK ∗Corresponding author (e-mail: [email protected]) Summary Networks are used to model real-world phenomena in various domains, including systems biology. Since proteins carry out biological processes by interacting with other proteins, it is expected that cellular functions are reflected in the structure of protein-protein inter- action (PPI) networks. Similarly, the topology of residue interaction graphs (RIGs) that model proteins’ 3-dimensional structure might provide insights into protein folding, sta- bility, and function. An important step towards understanding these networks is finding an adequate network model, since models can be exploited algorithmically as well as used for predicting missing data. Evaluating the fit of a model network to the data is a formidable challenge, since network comparisons are computationally infeasible and thus have to rely on heuristics, or “network properties.” We show that it is difficult to assess the reliability of the fit of a model using any network property alone. Thus, we present an integrative approach that feeds a variety of network properties into five machine learning classifiers to predict the best-fitting network model for PPI networks and RIGs. We confirm that ge- ometric random graphs (GEO) are the best-fitting model for RIGs. Since GEO networks model spatial relationships between objects and are thus expected to replicate well the un- derlying structure of spatially packed residues in a protein, the good fit of GEO to RIGs validates our approach.
    [Show full text]
  • Communities and Homology in Protein-Protein Interactions
    Communities and Homology in Protein-protein Interactions Anna Lewis Balliol College University of Oxford A thesis submitted for the degree of Doctor of Philosophy Michaelmas 2011 2 3 This thesis is dedicated to the inspirational Jen Weterings. Wishing her well in her ongoing recovery. Acknowledgements With thanks to Charlotte, Nick and Mason, for being the best supervisors a girl could ask for. With thanks to all those who have helped me with the work in this thesis. In particular Sumeet Agarwal, Rebecca Hamer, Gesine Reinert, James Wakefield, Simon Myers, Steve Kelly, Nicholas Lewis, members of the Oxford Protein Informatics Group and members of the Oxford/Imperial Systems and Signalling group. With thanks to all those who have made my DPhil years a wonderful experience, in particular my family, my Balliol family, and my DTC family. Abstract Knowledge of protein sequences has exploded, but knowledge of protein function is needed to make use of sequence information, and this lags behind. A protein’s function must be understood in context and part of this is the network of interactions between proteins. What are the relationships between protein function and the structure of the interaction network? In the first part of my thesis, I investigate the functional relevance of clusters, or communities, of proteins in the yeast protein interaction network. Communities are candidates for biological modules. The work I present is the first to systematically investigate this structure at multiple scales in such networks. I develop novel tests to assess whether communities are functionally homogeneous, and demonstrate that almost every protein is found in a functionally homogeneous community at some scale.
    [Show full text]
  • The Structure and Function of Complex Networks∗
    SIAM REVIEW c 2003 Society for Industrial and Applied Mathematics Vol. 45,No. 2,pp. 167–256 The Structure and Function of Complex Networks∗ M. E. J. Newman† Abstract. Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks. Key words. networks, graph theory, complex systems, computer networks, social networks, random graphs, percolation theory AMS subject classifications. 05C75, 05C90, 94C15 PII. S0036144503424804 Contents. 1 Introduction 168 1.1 Types of Networks ............................. 171 1.2 Other Resources .............................. 172 1.3 Outline of the Review ........................... 174 2 Networks in the Real World 174 2.1 Social Networks ............................... 174 2.2 Information Networks ........................... 176 2.3 Technological Networks .......................... 178 2.4 Biological Networks ............................ 179 3 Properties of Networks 180 3.1 The Small-World Effect .......................... 180 3.2 Transitivity or Clustering ......................... 183 3.3 Degree Distributions ............................ 185 3.3.1 Scale-Free Networks ........................ 186 3.3.2 Maximum Degree .......................... 188 3.4 Network Resilience ............................. 189 3.5 Mixing Patterns .............................. 190 ∗Received by the editors January 20, 2003; accepted for publication (in revised form) March 17, 2003; published electronically May 2, 2003. This work was supported in part by the U.S. National Science Foundation under grants DMS-0109086 and DMS-0234188 and by the James S.
    [Show full text]
  • Coupling AI and Network Biology
    Coupling AI and network biology Generate insights for disease understanding and target identification Alexandr Ivliev, Director of Bioinformatics Cheng Fang, Scientific Consultant 03.06.2020 Agenda 1. Introduction 2. Coupling AI and network biology 3. High-quality biological networks in microbiome for target ID 4. Key takeaways Introduction © 2020 Clarivate 3 Genomic revolution of early 2000’s From individual genes to understanding entire genome © 2020 Clarivate 4 Artificial intelligence: new ongoing revolution Revolutionizing industries Computer Natural language Reinforcement vision processing learning • Self-driving cars • Machine translation • Chess, go, computer games • Face recognition • Speech analysis • Robotics • And more • And more • And more © 2020 Clarivate 5 Artificial intelligence is a hot field First time “deep learning” appeared in Gartner Hype Cycle for Emerging Technologies in 2017 © 2020 Clarivate 6 Deep learning is a big field https://www.asimovinstitute.org/neural-network-zoo/ © 2020 Clarivate 7 Computer vision and image processing Esteva et al, Nat Med, 2019 © 2020 Clarivate 8 Text mining, e.g. electronic health records Esteva et al, Nat Med, 2019 © 2020 Clarivate 9 Applications in genomics Esteva et al, Nat Med, 2019 © 2020 Clarivate 10 Networks are how biology works Drug target • Disease mechanism understanding Disease genes • Target ID Network by Martin Grandjean © 2020 Clarivate 11 Can biological networks be coupled with deep neural networks to enable disease mechanism understanding and target ID? Target © 2020 Clarivate 12 What approaches are you taking to understand disease mechanisms and identify novel drug targets? a. Literature searches b. OMICs data analysis c. Small scale lab experiments d. Classical machine learning e. Deep learning f.
    [Show full text]
  • Network Biology: Understanding the Cell’S Functional Organization
    REVIEWS NETWORK BIOLOGY: UNDERSTANDING THE CELL’S FUNCTIONAL ORGANIZATION Albert-László Barabási* & Zoltán N. Oltvai‡ A key aim of postgenomic biomedical research is to systematically catalogue all molecules and their interactions within a living cell. There is a clear need to understand how these molecules and the interactions between them determine the function of this enormously complex machinery, both in isolation and when surrounded by other cells. Rapid advances in network biology indicate that cellular networks are governed by universal laws and offer a new conceptual framework that could potentially revolutionize our view of biology and disease pathologies in the twenty-first century. PROTEIN CHIPS Reductionism, which has dominated biological research programme to map out, understand and model in quan- Similar to cDNA microarrays, for over a century, has provided a wealth of knowledge tifiable terms the topological and dynamic properties of the this evolving technology about individual cellular components and their func- various networks that control the behaviour of the cell. involves arraying a genomic set tions. Despite its enormous success, it is increasingly Help along the way is provided by the rapidly develop- of proteins on a solid surface without denaturing them. The clear that a discrete biological function can only rarely ing theory of complex networks that, in the past few proteins are arrayed at a high be attributed to an individual molecule. Instead, most years, has made advances towards uncovering the orga- enough density for the biological characteristics arise from complex interac- nizing principles that govern the formation and evolution detection of activity, binding tions between the cell’s numerous constituents, such as of various complex technological and social networks9–12.
    [Show full text]
  • Biological Network Analysis Has Become a Central Component of Computational and Systems Biology
    Pacific Symposium on Biocomputing 15:120-122(2010) DYNAMICS OF BIOLOGICAL NETWORKS: SESSION INTRODUCTION TANYA Y. BERGER-WOLF1 Department of Computer Science, University of Illinois at Chicago Chicago IL 60607, USA TERESA M. PRZYTYCKA2 National Center of Biotechnology Information, NLM, NIH Bethesda MD 20814, USA MONA SINGH 3 Department of Computer Science, Lewis Sigler Institute for Integrative Genomics Princeton University, Princeton NJ 08544, USA DONNA K. SLONIM 4 Department of Computer Science, Tufts University Department of Pathology, Tufts University School of Medicine Medford, MA 02155 Biological network analysis has become a central component of computational and systems biology. Because such analysis provides a unifying language to describe relations within complex systems, it has played an increasingly important role in understanding physiological function. Significant efforts have focused on analyzing and inferring the topology and structure of cellular networks and on relating them to cellular function and organization. However, much of this work has taken a static view of cellular networks, despite the knowledge that biological networks can change with time, context, and conditions. We introduce this session on The Dynamics of Biological Networks to encourage and support the development of computational methods that elucidate the dynamic interactome. Biological networks encompass many types of variation. Temporal variation can be inferred via experimentally determined large-scale (static) cellular networks, along with other high- throughput experimental data sets that provide snapshots of biological systems at different times and conditions. These data are often integrated with static interaction data (e.g. protein-protein, domain-domain, or regulatory interactions), time- or environment-dependent expression data, protein localization data, or other contextual information.
    [Show full text]
  • Representation Learning for Networks in Biology and Medicine: Advancements, Challenges, and Opportunities Arxiv:2104.04883V1 [C
    Representation Learning for Networks in Biology and Medicine: Advancements, Challenges, and Opportunities Michelle M. Li1,3, Kexin Huang2, and Marinka Zitnik3,4,5,∗ 1Bioinformatics and Integrative Genomics Program, Harvard Medical School 2Health Data Science Program, Harvard T.H. Chan School of Public Health 3Department of Biomedical Informatics, Harvard Medical School 4Broad Institute of MIT and Harvard 5Harvard Data Science ∗Correspondence: [email protected] Abstract With the remarkable success of representation learning in providing powerful predictions and data in- sights, we have witnessed a rapid expansion of representation learning techniques into modeling, analysis, and learning with networks. Biomedical networks are universal descriptors of systems of interacting el- ements, from protein interactions to disease networks, all the way to healthcare systems and scientific knowledge. In this review, we put forward an observation that long-standing principles of network biology and medicine—while often unspoken in machine learning research—can provide the conceptual grounding for representation learning, explain its current successes and limitations, and inform future advances. We synthesize a spectrum of algorithmic approaches that, at their core, leverage topological features to embed networks into compact vector spaces. We also provide a taxonomy of biomedical areas that are likely to benefit most from algorithmic innovation. Representation learning techniques are becoming essential for identifying causal variants underlying complex traits, disentangling behaviors of single cells and their impact on health, and diagnosing and treating diseases with safe and effective medicines. arXiv:2104.04883v1 [cs.LG] 11 Apr 2021 1 Introduction Networks, or graphs, are pervasive in biology and medicine, from molecular interaction maps to dependen- cies between diseases in a person, all the way to populations encompassing social and health interactions.
    [Show full text]